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Vol. 1, No. 4, 2020

Corresponding author:
1 Odessa National Economic University, Ukraine.
E-mail: kovalskiy_a@i.ua
ORCID: https://orcid.org/0000-0002-2243-0234

DOI: https://doi.org/10.30525/2661-5150/2020-4-14

METHODS OF RISK MANAGEMENT OF INVESTMENT PROJECTS’ 
EXPERTISE OF MUNICIPAL INFRASTRUCTURE ENTERPRISES

Andrii Kovalskyi1

Abstract. The issue of risk assessment of investment projects at the state level is not given much attention 
and there is no proposed method for assessing such risks. Considering the transition of public utilities under 
the conditions of decentralisation to the need for self-sufficiency, the latter must use a well-established 
methodology for assessing risks and uncertainties, which is carried out by private sector entities expert 
assessments, or methods of mathematical statistics when evaluating their investment projects. A partial 
answer to the lack of a methodology for assessing the risk levels of investment projects should be the concept 
of modelling decision-making under uncertainty. The concept of modelling decision-making is based on 
two essential properties that constitute the very essence of the modelling process. Firstly, the model must 
be similar to the object under study; secondly, it must be more direct than the object under study to be 
considered. The main purpose of the model is the ability to conduct experiments with the model, analysis 
and study, which are impossible with the object under study. The paper develops the concept of modelling 
decision-making in conditions of uncertainty for investment projects’ expertise of municipal infrastructure 
enterprises, the essence of which is to develop different scenarios for the business entity using the technique 
of modelling decision-making, taking into account different parameters and characteristics under uncertainty. 
Uncertainty decision-that decision-making is based on the fact that the probabilities of different scenarios for 
the entity making the risk decision are unknown.

Key words: decision-making, technique of modelling, municipal infrastructure enterprises, forecast, uncertainty.

JEL Classification: D81, O18, J11, D81

1. Introduction
The decision-making process is an integral part of 

any managerial influence. Along with information 
processing, decision-making becomes a key factor in 
determining the effectiveness of strategic planning and 
forecasting. At the same time, the choice of specific 
decisions in the framework of strategic forecasting is 
often closely related to risks because of the unknown 
specific behaviour of the initial parameters, which do 
not allow to determine the value of the final results of 
these decisions clearly.

It should also be taken into account that decision-
making is the result of specific management 
activities, a creative process based on the principles 
of consistency and rationality aimed at choosing the 
best course of action. The task of decision-making 
arises when there is a goal to be achieved, there are 
different ways to achieve it, and there are factors 
that limit the ability to achieve the goal. In essence, 
the decision goes through the following stages  
(Figure 1).

Analysing the presented scheme, it should be 
noted that the decision-making process is cyclical, in 
addition, this scheme is an idealised model because 
due to the variety of situations and problems that 
need to be solved, the real decision-making processes 
usually differ from it, it means the actual structure of 
management decision-making largely determined by 
the situation.

At the same time, decisions made in the field of 
strategic forecasting should be based on data from 
future periods. Of course, it is physically impossible to 
do this, which is why it is often necessary to operate 
with data from past periods, as well as information 
about the current situation, extrapolating them over 
time. It turns out that the forecasting data already 
contain a significant share of uncertainty due to their 
very nature.

Depending on the degree of uncertainty of future 
behaviour of the initial decision-making parameters, 
there are risk conditions under which the probability 
of occurrence of individual events affecting the final 
result can be established with some degree of accuracy, 



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Analysis 
of the 

situation Problems 
identifi-
cation

Goals 
setting

Monitoring
and data 

collection

Formation
of options 

for 
possible 
solutions 

Evaluation
of 

decisions 
by criteria

Decision 
evaluation

Choosing 
the best 
solution 

Planning 

Implemen-
tation

Evaluation
of results

and uncertainty conditions in which such probability 
cannot be established.

Modelling as a method of research of control 
systems is used in the development of quite complex 
management decisions and is the construction of 
models of the studied object for its study. The study 
of object models allows to clarify the properties and 
characteristics of the phenomenon under study.

Like all tools and methods, the decision model can 
contain errors. The main reason for their occurrence 
is the inaccuracy of initial assumptions. Because any 
model is based on some initial and other assumptions, 
some of them can be estimated and can be objectively 
verified and calculated. At the same time, some 
preconditions are not measurable and cannot be 
objectively verified, in particular in the conditions 
of insufficient initial information. Since such 
assumptions are the basis of the model, the accuracy of 
the latter depends on the accuracy of the assumptions. 
The model cannot be used to forecast, for example, 
inventory requirements if sales forecasts for the next 
period are inaccurate.

Figure 1. Stages of decision making in conditions of uncertainty

In addition, there may be information uncertainty, 
which may be caused by either incompleteness or 
redundancy of the original data.

Uncertainty decision-making is based on the fact that 
the probabilities of different scenarios for the entity 
making the risk decision are unknown. In this case, 
choosing an alternative solution, the subject is guided, 
on the one hand, by the advantage of risk, and on the 
other hand, by the appropriate selection criteria from all 
alternatives in accordance with its “decision matrix”.

The task of decision-making under uncertainty is the 
task of choosing the optimal strategy, the result of which, 
among other things, depends on many uncertain factors, 
resulting in each specific strategy (decision) corresponds 
not to a single outcome but many outcomes.

2. Methodology for modelling  
decision making under uncertainty  
for investment projects’ expertise  
of municipal infrastructure enterprises

Consider the classic decision-making criteria under 
uncertainty (Table 1)



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Table 1
Criteria for decision-making under uncertainty

Criteria Сore Conclusions

Wald criterion

According to this criterion, playing 
with “nature” (external conditions, 
“environment”) is a game with an aggressive 
and intelligent opponent. Choose a strategy 
with an index for which the position is 
a position of extreme pessimism. It is 
reinsurance for the decision maker.

Wald criterion is acceptable when the decision-making 
situation has the following features:
– nothing is known about the possibility of implementing 
“nature” (external conditions, “environment”) of their 
strategies;
– it is necessary to take into account different strategies 
of “nature”;
– the decision is unique, it can be made only once;
– any risk must be eliminated.

Maximax criterion

The simplest variant of uncertainty is 
“benign” stochastic. In this case, the optimal 
strategy is the one for which the criterion 
reaches a maximum.

It is assumed that the decision-making situation has the 
following properties:
– the probabilities of applying “nature” strategies are 
unknown and do not depend on time;
– decisions are made (theoretically) infinitely many 
times;
– for a small number of implementations, the solution 
involves some risk.

Savage criterion 

This is also a rather pessimistic criterion, as 
well as the maximin criterion. However, in 
the case of choosing the optimal strategy, it 
focuses on minimal risk.

Savage criterion should be used when it is necessary 
to choose a strategy that will protect against excessive 
losses. Savage test is used when there is confidence that a 
possible loss will not lead to a complete collapse.

Hurwitz criterion (criterion of 
“optimism-pessimism” or “alpha 
criterion”) 

According to this criterion, when choosing a 
solution, one should not focus on pessimism 
or optimism. It is necessary to take a certain 
combination of them, setting the coefficient 
of optimism.

The criterion allows to take into account the level of 
optimism (riskiness) of the decision maker. This makes 
this criterion more acceptable before the maximin and 
maximax criteria.

Laplace criterion

This criterion makes it possible to identify 
the best solution in the case when none of 
the conditions of “nature” has a significant 
advantage.

The criterion should be used when each state of “nature” 
is equally probable compared to others. In this case, the 
optimal alternative is the one with the highest average 
score.

3. Application of the methodology  
for modelling decision making under 
uncertainty for investment projects’ expertise 
of municipal infrastructure enterprises

We will carry out the procedure of selecting one of 
a number of alternative market segments to promote 
new services of the municipal enterprise (ME) 
“Odesmiskelektrotrans”, which plans to purchase 
electric buses for use in its activities. To increase the 
efficiency and investment attractiveness of the company, 
it is advisable to develop other activities. 

Based on the specifics of consumer demand, segment 
capacity, profitability, etc., acceptable, in addition to the 
main activity, are four segments (corporate services, 
schools and other educational institutions, rental of 
vehicles, excursions). It is known that when targeting 
each of the market segments, a number of alternative 
results can be realised, which differ in the size of the 
profit. The differences in the results are explained by 
different scenarios in selected target market segments.

Possible solutions (choice of a specific segment) and 
their consequences (results – average annual profit) are 
formally given in Table 2.

Table 2
Decision (win) matrix

Alternatives
Possible results

Y1 ... Yj … Ym
Х1 q11 ... q1j … q1m
... ... ... ... ... ...
Хі qi1 ... qij ... qim
… … ... … … …
Хn qn1 ... qnj … qnm

As follows from Table 2, each of the alternative 
solutions may lead to certain consequences. Many of 
these consequences have been identified, but which of 
them are realised at the time of the decision is unknown. 
This is the element of uncertainty and risk.

Alternatives cannot be compared by any estimate, as 
it is not known what result is realised. It is necessary 
to evaluate the whole set of values of the results for 
each alternative, which is generally a row of the matrix 
(Table 2).

After that, you can compare the alternatives for this 
comprehensive assessment. Thus, you can choose the 
best alternative not for any particular result, but for the 
whole set of results because it is unknown which of them 



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will happen. We will carry out the procedure of choosing 
the best alternative for ME “Odesmiskelektrotrans”.

We have calculated the amount of profit that the 
company can get from entering different segments of 
the transportation market; the results are presented in 
Table 3.

Table 3
Alternative options of the target market segment  
and their consequences (profit) in different 
conditions of the volume of traffic, thousand UAH

Market segments
Volume of traffic, thousand UAH

15.0 25.0 35.0 45.0
Schools and other 
educational institutions

72.3 93.0 95.2 102.1

Corporate services 75.5 94.0 134.0 178.4
Rental of vehicles 74.1 96.5 112.7 135.2
Excursions 83.8 87.4 99.0 97.0

Wald criterion is designed to choose from the 
considered options of strategies the option with the 
highest efficiency indicator from the minimum possible 
indicators for each of these options. This criterion 
maximises the minimum gain that can be obtained in 
the implementation of each of the options.

The criterion orients the decision maker to a cautious 
course of action aimed at generating income and 
minimizing possible risks at the same time. That is, 
it corresponds to a pessimistic type of behaviour in 
conditions of uncertainty.

According to Wald criterion, the preferred alternative 
is X *, which satisfies the conditions:
1) for the matrix of acquisitions
X max min qi j ij

* = �
2) for the loss matrix
X minmax qi j ij

* = �
It is seen that the best of the worst indicators has the 

alternative Excursions; for it qij = 83.8 
the most: 
X maxi
* , ; , ; , ; , ,= ( ) =� 72 3 75 5 74 1 83 8 83 8

The maximax criterion is based on the idea that the 
decision maker, having the opportunity to manage 
the situation to some extent, expects that there will be 
a development of the situation that is most beneficial. 
That is, it corresponds to a suboptimistic type of 
behaviour.

According to this criterion, the best of the alternatives 
is selected by the rules:
1) for the matrix of acquisitions
X max max qi j ij

* = �
2) for the loss matrix
X minminx qi j ij

* = �
Thus, in our variant the alternative corresponding 

to the maximum element of a matrix of winnings is 
accepted:

X maxi
* , ; , ; , ; , ,= ( ) =� 102 1178 4 135 2 99 0 178 4

Thus, the best of the best indicators has the alternative 
“Corporate Services”, for which qij =178.4 the most. 

In order to apply Savage criterion, it is necessary 
to construct a risk matrix. Based on the risk matrix, 
the best alternative would be the one that can lead to 
minimal losses.

The results of calculations of the risk matrix are 
presented in Table 4.

According to Savage criterion, the alternative 
“Corporate Services” is optimal, as its implementation 
leads to the least negative consequences.

Hurwitz criterion focuses on striking a balance 
between cases of extreme pessimism and extreme 
optimism when choosing a strategy by weighing both 
finals using a coefficient of optimism (confidence).

The estimate ZI for the alternative Хi is calculated 
according to the rule:
Z max q minqi i ij i ij= + −( )� � � �α α* *1
The coefficient of optimism (trust) α shows how 

much the decision maker can manage the situation and 
to some extent counts on a favourable outcome.

If the probabilities of favorable and unfavourable 
situation for the decision maker are equal, then α = 0 5, .�
should be taken.

At α = 1, this criterion is converted into a maximax.  
If we choose α close to 0, then we follow a pessimistic 
type of behaviour, the least risky.

The best alternative is chosen according to the 
following rules:
1) for the matrix of acquisitions
X max Zi i
* ,= �  

2) for the loss matrix
X minZi i
* .= �  

Since in our conditions we do not have the opportunity 
to rely on a certain level of optimism of the decision 
maker, we will take it equal to α = 0 5, .  

Тhen: 
Z1 0 5 102 1 0 5 72 3 87 2= + =, * , , * , ,

Z2 0 5 178 4 0 5 75 5 127 0= + =, * , , * , ,

Z3 0 5 135 2 0 5 74 1 104 7= + =, * , , * , ,

Z4 0 5 99 0 0 5 83 8 91 4= + =, * , , * , ,

X maxi
* , ; , ; , ; , ,= ( ) =� �87 2 127 0 104 7 91 4 127 0

According to the calculations, you should choose the 
alternative “Corporate Services”.

Laplace criterion allows you to choose the best option 
for management decisions, based on equal probabilities 
of the external environment.

According to this criterion, the best of the alternatives 
is selected by the rules:
1) for the matrix of acquisitions
X max xqj ij

* = �



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2) for the loss matrix
X minx xqj ij

* = �
Then:

x1 1 4 72 3 93 0 95 2 102 1 90 7= + + +( ) =/ , , , , ,
x2 1 4 75 5 94 0 134 0 178 4 120 5= + + +( ) =/ , , , , ,
x3 1 4 74 1 96 5 112 7 135 2 104 6= + + +( ) =/ , , , , ,
x4 1 4 83 8 87 4 99 0 97 0 91 8= + + +( ) =/ , , , , , ,
X maxi
* , ; , ; , ; , ,= ( ) =� 9 7 120 5 104 6 91 8 120 5

According to the calculations, the alternative is 
“Corporate Services”, so it is advisable to choose it.

The results of the calculation of decision-making 
criteria allow us to conclude that the best option for ME 
“Odesmiskelektrotrans” is the alternative “Corporate 
Services”, as all criteria, except the Wald criterion, 
showed that it is the best.

Thus, we have managed to offer the utility a balanced 
and sound strategic decision on the choice of alternative 
development.

4. Conclusions
The technique of modelling decision-making, taking 

into account various parameters and characteristics, 
in conditions of uncertainty, justifies itself and allows 
for qualitative analysis and strategic forecasting of 

the company’s development. Modern approaches to 
forecasting development make it possible to take into 
account any possible options for the development of 
the situation, as well as to simplify the construction of 
a model for making sound management decisions.

The paper develops the concept of modelling decision-
making in conditions of uncertainty, the essence of 
which is to develop different scenarios for the business 
entity using the technique of modelling decision-
making, taking into account different parameters 
and characteristics in conditions of uncertainty. 
Uncertainty decision-making is based on the fact that 
the probabilities of different scenarios for the entity 
making the risk decision are unknown. In this case, 
choosing an alternative solution, the subject is guided, 
on the one hand, by the advantage of risk, and on the 
other hand, by the appropriate selection criteria from all 
alternatives in accordance with its “decision matrix”. The 
task of decision-making in conditions of uncertainty is 
the task of choosing the optimal strategy, the result of  
which, among other things, depends on many uncertain 
factors, as a result of which each strategy (decision) 
corresponds not only to a single result, but many results.

Based on the calculation of decision-making criteria in 
conditions of uncertainty ME “Odesmiskelektrotrans” 
proposed a balanced and sound strategic decision on 
the choice of alternative development.

Table 4
Risk matrix

Market segments
Profit in terms of traffic volume, thousand UAH Risk matrix in terms of traffic volume, thousand UAH
15.0 25.0 35.0 45.0 15.0 25.0 35.0 45.0

Schools and other 
educational institutions

72.3 93.0 95.2 102.1 11.5 3.5 38.8 66.3

Corporate services 75.5 94.0 134.0 178.4 8.3 2.5 0 0
Rental of vehicles 74.1 96.5 112.7 135.2 9.7 0 21.3 43.2
Excursions 83.8 87.4 99.0 97.0 0 9.1 35.0 81.4

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